design and analysis of microarray experiments at csiro livestock industries

Design and Analysis ofMicroarray Experiments atCSIRO Livestock Industries

Toni Reverter

Bioinformatics GroupCSIRO Livestock Industries

Queensland Bioscience Precinct306 Carmody Rd., St. Lucia, QLD 4067, Australia

SSAI – QLD Branch – 6 Apr. 2004


Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

CONTENTS

1. Introduction …………………………… 4 62. Technical Concerns ……...……………. 2 73. Designs ………………..………………. 21 154. Analysis ……………..………………… 14 165. Coverage and Sensitivity ...……………. 5 76. Summary …………....………………… 2 4

Slides Minutes



1. Introduction

1.a – The Material

This is a Cow

This is a Sheep

This is a Pig(female)

This is a Chicken



cDNA “A” Cy5 cDNA “B” Cy3

Tissue Samples

Treat A Treat B

mRNA Extraction & Amplification

Hybridization

Laser 1 Laser 2

Optical Scanner

+

Image Capture

Analysis

1.b - The Method1. Introduction


1.c - The Challenge


Time Dependent

Chronology

Logical

1800s – DATA30-60s – METHODS50-70s – SOFTWARE1980s – COMPUTER

cDNA

Human Dependent

Skill Integration

QuantitativeComputer Sci.StatisticiansMathematicians …….

Non-QBiochemistsPhysiologistsPathologists …….

BANANA EGG

“banana omelette”

Historical Excitement Balance Interdisciplinary

Data Dependent

Paradigm

Distribution

Source Size

1. Introduction



The Biologist and the Statistician are being executed.They are both granted one last request.

The Statistician asks that he/she be allowed to give onefinal lecture on his/her Grand Theory of Statistics.The Biologist asks that he/she be executed first.

JOKE

“The majority of microarray papersare analysed with substandard methods”

C Tilstone (citing D Allison), Nature 2003, 424:610

CLAIM

1. Biologists don’t care ………………………………… 102. Statisticians are bad …………………………………. 203. Unrealistic expectations ……………………………… 70

REASONS P Value

1.c – Human-Dependent Challenge1. Introduction



Replication:1. Animal2. Sample3. Array4. Spot

1. Biochemist Level:a. Preparation (Printing) of the Chipb. RNA Extraction, Amplification and Hybridisationc. Optical Scanner (Reading)

2. Quantitative Level:a. Designb. Image (data) Qualityc. Data Analysisd. Data Storage

2. Technical Concerns

Note: Randomisation intentionally neglected.



2.a – Data Quality: GP3xCLI 2.b – Storage: GEXEX

2. Technical Concerns



a. Identify/Prioritise Questionsb. N of Available Samplesc. N of Available Arraysd. Consider Dye Bias

Key Issues:

Put more arrayson key questions

3. Experimental Designs

Pooling?

•Dye-Swap•Dye-Balancing•Self-Self

O

B

A

ABReference

Evaluation of Designs:

O

B

A

ABLoop

O

B

A

ABAll-Pairs

Variance of Estimated Effects (Relative to the All-Pairs)

Reference

1132

Loop

4/31

8/31

All-Pairs

1121

Main effect of AMain effect of BInteraction ABContrast A-B



Glonek & Solomon Factorial and Time Course Designs for cDNA Microarray Experiments

• DefinitionA design with a total of n slides and design matrix X is said to be admissibleif there exists no other design with n slides and design matrix X* such that

ci* ciFor all i with strict inequality for at least one i. Where ci* and ci are respectivelythe diagonal elements of (X*’X*)-1 and (X’X)-1.

• Samples vs Slides vs Configurations

3 4 12

2

6

3

12

11

132

(S-1)

S(S-1)

Samples (S)

Arr

ays

N of Configurations?




SA-1





Pie-Bald black Non-Pie-Bald black

Normal

White

Recessive SA-1 = 53 = 125





x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5




0 hr 24 hr

SA-1 = 109 = 1 Billion!





Opt 1: 10 Slides Opt 2: 10 Slides Opt 3: 11 Slides

Opt 4: 9 Slides Opt 5: 9 Slides

Transitivity (Townsend, 2003) & Extendability (Kerr, 2003)3. Experimental Designs



0 hr 24 hr


SA-1 = 1210 = 62 Billion!




0 hr 24 hr

R

R

R R

R

R

R

R

RR

R

R

G

G

G G

G

G

G

G

G

G

G

G





Pavlidis et al.(2003) The effect of replication on geneExpression microarray experiments. Bioinformatics 19:1620

>= 5 Replicates10-15 Replicates

Peng et al.(2003) Statistical implications of pooling RNASamples for microarray experiments. BMC Bioinformatics 4:26

Power: n9c9 95%, n3c3 50%, n9c3 90% n25c5 n20c20

Handling Constraints (Samples & Arrays):


N of Arrays?



F HS

M TM

F HS

M HS

F TM

M HS

F HS

M HS

R

R

R

R

R

R

R

R

R

R

R

R

R

R

G

GG

G

G

G

G

G

G

G

G

G

G

G

24: 23 To 552

14: 13 To 182

pooling




RES SUS 0 3 24 M F HS TM

RES 8 -8 1 0 -1 -1.766 1.766 -3.866 3.866

SUS 8 -1 0 1 1.766 -1.766 3.866 -3.866

0 8 -4 -4 -1.335 1.335 0.666 -0.666

3 10 -6 -1.033 1.033 -0.468 0.468

24 10 2.368 -2.368 -0.198 0.198

M 6.247 -6.247 0.493 -0.493

F 6.247 -0.493 0.493

HS 3.798 -3.798

TM 3.798

Sum(ABS) 29.3 29.3 22.0 23.0 27.1 21.7 21.7 17.6 17.6

Sum(ABS) 26.8 26.8 39.1 23.1 17.3 7.1 7.1 14.3 14.3

Reference Design




Another (NEW?) Constraint:

A

B

C

D

E

M avium slope 18 days 3 3-3-3

M avium broth 18 days 10 1-2-2-1-2-1-2-1-2-1

M para broth 10 weeks 5 1-2-2-1-1

M para broth 12 weeks 6 1-1-4-5-2-1

M para in-vivo 3 1-1-1




A B

C

D

E

A

A

A

B

B

B

C

D

E

C

C

D

E

D E

Importance due to Transitivity of AB with BC and BD

Procedure:Five configurations will be proposed and the statistical optimality of each evaluated.

Another (NEW?) Constraint:




3 3 3

1 2 2 1 2 1 2 1 2 1

1 2 2 1 1

1 1 4 5 2 1

1 1 1



3 3 3

1 2 2 1 2 1 2 1 2 1

1 2 2 1 1

1 1 4 5 2 1

1 1 1

Configuration 1



3 3 3

1 2 2 1 2 1 2 1 2 1

1 2 2 1 1

1 1 4 5 2 1

1 1 1

Configuration 2



3 3 3

1 2 2 1 2 1 2 1 2 1

1 2 2 1 1

1 1 4 5 2 1

1 1 1

Configuration 3



3 3 3

1 2 2 1 2 1 2 1 2 1

1 2 2 1 1

1 1 4 5 2 1

1 1 1

Configuration 4



3 3 3

1 2 2 1 2 1 2 1 2 1

1 2 2 1 1

1 1 4 5 2 1

1 1 1

Configuration 5



A B

C

D

E

A

A

A

B

B

B

C

D

E

C

C

D

E

D E

Imp Weight Squared Error

1 2 3 4 5 1 2 3 4 5

4 6 5 6 6 5 4 1 4 4 1

2 0 2 1 0 0 4 0 1 4 4

2 3 2 2 3 4 1 0 0 1 4

1 0 0 0 0 0 1 1 1 1 1

3 5 5 4 4 5 4 4 1 1 4

4 4 5 5 5 5 0 1 1 1 1

1 0 0 0 0 0 1 1 1 1 1

2 2 0 2 3 2 0 4 0 1 0

1 0 0 0 0 0 1 1 1 1 1

4 3 3 3 3 3 1 1 1 1 1 SSE 17 14 11 16 18

0 1 2 1 0 0 MSE .74 .64 .48 .66 .75

NoiseD D

Con

clu

sion

: C

onfi

gura

tion

3



1. Relaxed data acquisition criteriaa. Signal to Noise > 1.00 (relaxer (sp?) exist)b. Mean to Median > 0.85 (Tran et al. 2002)

2. Moving away froma. Ratiosb. “heavy-duty” normalisation techniques

3. Mixed-Model Equationsa. Check residualsb. Check REML estimates of Variance Componentsc. Proportion of Total V due to Gene x Variety

4. Process results Gene x Treatmenta. Mixtures of Distributions

4. Data Analysis

My (EDUCATED?) View:



eTv

Ta

Tg VVAAGGXMVNY ,~

Log2Intensities

Comparison GroupArray|Block|Dye

(FIXED) Main GeneEffect(RANDOM)

Gene x Dye(RANDOM)

Gene xVariety(RANDOM)

Residual(RANDOM)

DE Genes

Note: missing but (generally) unimportant.

Gene xArray|Block(RANDOM)

4. Data AnalysisMixed-Model Equations



Mixed-Model Equations

Log2(Int.) = CG + Gene + GDye + GArray + GVariety + Error

The proportion of the Total Variationaccounted for by the G x Variety Interactionanticipates the proportion of DE Genes

CLAIMControl

ofFDR

4. Data Analysis



Y11 197,802 9.33 1.99 5.17 15.99 768 257.5 139 343

Y12 74,030 10.82 1.91 4.95 15.99 576 128.5 22 243

Y21 110,308 9.99 2.07 4.25 15.99 576 191.5 27 319

Y22 116,409 9.89 2.09 5.17 15.99 576 202.1 19 318

Y23 117,687 10.38 2.04 4.91 15.99 576 204.3 36 320

Y31 106,591 10.11 1.77 6.60 15.99 672 158.6 37 278

Y32 236,671 9.44 2.11 5.36 15.99 1,440 164.3 57 269

Observations Comparison Groups Levels ObservationsN Mean SD Min Max Mean Min Max

4. Data Analysis



54 Array Slides

959,498 Valid Intensity Records (S2N>1, M2M>0.85)

7,638 Elements (genes)

752,476 Equations

56 (Co)Variance Components (REML)

BAYESMIX (Bayesian Mixtures of distributions)

4. Data Analysis



2

2

2

2

2

2

2

77,67,57,47,37,27,1

7,667,56,46,36,26,1

7,56,555,45,35,25,1

7,46,45,444,34,24,1

7,36,35,34,333,23,1

7,26,25,24,23,222,1

7,16,15,14,13,12,11

ggggggg

ggggggg

ggggggg

ggggggg

ggggggg

ggggggg

ggggggg

g

2

2

2

2

2

2

2

7

6

55,45,3

5,444,3

5,34,33

2

1

000000

000000

0000

0000

0000

000000

000000

a

a

aaa

aaa

aaa

a

a

a

2

2

2

2

2

2

2

7

6

55,45,3

5,444,3

5,34,33

22,1

2,11

000000

000000

0000

0000

0000

00000

00000

v

v

vvv

vvv

vvv

vv

vv

v

2222222

7654321 eeeeeeee diag

56 (Co)Variance Components4. Data Analysis



% TotalVarianceDue to:

Error 3.0 – 3.6 5.1 – 6.7 3.0 – 3.7

Gene 83.6 – 90.4 78.3 – 81.9 47.5 – 83.9

Gene x Array 3.5 – 9.8 10.4 – 12.6 10.6 – 43.5

Gene x Variety 2.4 – 3.7 2.1 – 2.6 2.5 – 5.4

Genetic Correlations Moderate (EXP3) to Strong

Gene Variety Corr Strong (EXP1) to Moderate (EXP2)

4. Data Analysis



2

1

)(ˆ)(ˆ2

11

jijiji LOWvHIGHvd

5

3

)2(ˆ)1(ˆ3

12

jijiji BREEDvBREEDvd

7

6

5

0

)(ˆ)(ˆ12

13

j tijiji CONTROLvTREATMENTvd

i = 1, …, 7,638 genesj = 1, …, 7 variablest = 0, …, 5 time points (EXP3 only)

Other measure definitions could also be valid

Measures of (Possible) Differential Expression4. Data Analysis



.

38.006.005.0

06.016.002.0

05.002.008.0

,

23.0

08.0

08.0

10.0

08.001.004.0

01.011.009.0

04.009.067.0

,

01.0

19.0

40.0

23.0

02.001.001.0

01.004.001.0

01.001.010.0

,

01.0

03.0

21.0

67.0

3

2

1

N

N

N

d

d

d

f

4. Data AnalysisMixtures of Distributions



Mixtures of Distributions4. Data Analysis



Exp1 Exp2 Exp3 Up Down Up Down Up Down

High-Low Up 409 0 26 13 36 11Down 41 3 0 5 0

HOL-JBL Up 68 0 0 8Down 319 10 6

TSS-UTS Up 252 0Down 109

10 DE Elements across the 3 Exp(2 UP/DOWN/UP; 8 UP/UP/DOWN)

Differentially Expressed Genes4. Data Analysis



Residuals Plots4. Data Analysis

178 @ Day 82

139 @ Day 120

114

@ D

ay 1

05

171

@ I

ngui

nal

123 55

68 71

75

39

41

130

43129330

55164523

22

53

27

12

36

5

31

9926

14

4011

43

21

42

10

36

5

8124

25

12

46

12

36

5

26

12

36

5

44

22

Bovine

Ovine

Up-Regulated

Down-Regulated

Allocation of238 DE Genes



4. Data Analysis

HomologsOrthologsParalogs



The “Real” Target: Molecular Interaction Maps

Adapted from Aladjem et al. 2004, Sciences’s STKE

4. Data Analysis



MPSS Paper PNAS 03, 100:4702

tpm N Tags %

> 1 (0.0) 27,965 100.00 5 (0.7) 15,145 54.16 10 (1.0) 10,519 37.61 50 (1.7) 3,261 11.66 100 (2.0) 1,719 6.15 500 (2.7) 298 1.07 1,000 (3.0) 154 0.55 5,000 (3.7) 26 0.0910,000 (4.0) 7 0.02

MPSS Test Data No Tags = 25,503

S 1 S 2

100.00 100.00 57.14 49.87 36.11 33.66 10.89 10.74 5.73 5.67 1.21 1.13 0.57 0.55 0.15 0.11 0.05 0.05

cDNA Noise PaperPNAS 02, 99:14031

100.00 56.19 36.79 11.76 6.95 1.94 1.11 0.29 0.16

x

xxf

1

2exp)(

2

5. Coverage and Sensitivity

Let NT = N of “Total” GenesND = N of “Differentially Expressed” Genes (ND NT)

%

x

x

x

T

itt e

N

xnxf

1

2 2

)(

D

idd N

xnxf

)(

)(

)(

tT

dD

xfN

xfN

1. The relevance of f(xi) is limited to the Concentration Signal mapping.2. At equilibrium the probability of an error either way equals.

Flat line (except Upper Bound)

)()( tdT

D xfxfN

N

T

D

N

N

)()(

)(t

tT

dD xfxfN

xfN

it

idti xn

xnxfx

)(




< = >

Not many DE genesHigh ConfidenceFew False +ve

Lots of DE genesHigh PowerFew False -ve






General (ie. not only CSIRO LI):

1. Still in its infancy (…possibly even embryonic stage)2. Many decisions have a heuristic rather than a theoretical

foundation3. Prone to miss-conceptions:

a. Amount of Expression = Amount of Responseb. Same cut-off point to judge all genesc. Over-emphasis in normalization (hence, despise

“Boutique Arrays”)d. Over-emphasis in variance stabilizatione. Over-emphasis in controlling false-positivesf. Over-emphasis in biological replicates (DANGER )

4. No hope for a “One size fits all” software (even method)5. Safer to aim towards “Tailor to individual’s needs”6. Integration of interdisciplinary skills is a must

6. Summary



Livestock Species:

1. Tailing humans (…at the moment)a. Andersson & Georges (2004) Domestic-animal genomics:

Deciphering the genetics of complex traits. Nature Genetics, March 2004, Vol 5:202-212

2. Several key advantagesa. More relaxed ethical issues (…relative to R&D in humans)b. Very strong similarities at the genome level with humansc. The genome is (being) sequenced for several species

3. Strong background knowledge of genetics accumulateda. Quantitative geneticsb. Mixed-Model equationsc. Computing expertise

4. Journals will soon be inundated5. We have the opportunity to participate

6. Summary

design and analysis of microarray experiments at csiro livestock industries

Documents

csiro livestock industries1

introductionssai qld

challengessai qld branch

australiassai qld branch

materialssai qld branch

slidesminutesssai qld

csiro livestock industries2

design matrix x